**Title:** Human Angles

**Description:**
This lesson is designed to get your students moving! The lesson focuses primarily on transversals and angles. Students will be able to identify and relate some angles to cheer moves.
This is a College- and Career-Ready Standards showcase lesson plan.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**English Language Arts (10), or Mathematics (9 - 12)

**Title:**Human Angles

**Description:**This lesson is designed to get your students moving! The lesson focuses primarily on transversals and angles. Students will be able to identify and relate some angles to cheer moves. This is a College- and Career-Ready Standards showcase lesson plan.

**Title:** Card Table Project

**Description:**
Students will work in groups to design a card table. Students will communicate with each other through a class blog or class discussion page. Students will then work in groups to design a card table. After the design phase, students will try to sell their product to the outside expert.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics (9 - 12)

**Title:**Card Table Project

**Description:**Students will work in groups to design a card table. Students will communicate with each other through a class blog or class discussion page. Students will then work in groups to design a card table. After the design phase, students will try to sell their product to the outside expert.

**Title:** Creating a Water Tank - Part II "Selling the Tank"

**Description:**
Working in groups of 4-5 students will take the information,pictures and 3-D model of the water tank they assembled in Part I of Creating a Water Tank and develop a web page and a video presentation. The web page will be a tool to advertise their water tank construction company and must include hyperlinks and digital pictures. The video presentation will be a "sales pitch" to a city council. The web page and video will be scored using a rubric. The web page and video must include the surface area, volume and cost of construction.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics (7 - 12), or Technology Education (9 - 12)

**Title:**Creating a Water Tank - Part II "Selling the Tank"

**Description:**Working in groups of 4-5 students will take the information,pictures and 3-D model of the water tank they assembled in Part I of Creating a Water Tank and develop a web page and a video presentation. The web page will be a tool to advertise their water tank construction company and must include hyperlinks and digital pictures. The video presentation will be a "sales pitch" to a city council. The web page and video will be scored using a rubric. The web page and video must include the surface area, volume and cost of construction.

**Title:** Golden Ratios of the Body, Architecture, and Nature

**Description:**
Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
**Standard(s): **

[MA2015] (6) 24: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. [6-G4]

**Subject:**Mathematics (6 - 12), or Technology Education (9 - 12)

**Title:**Golden Ratios of the Body, Architecture, and Nature

**Description:**Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.

**Title:** Swimming Pool Math

**Description:**
Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
**Standard(s): **

[MA2015] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. [8-G9]

**Subject:**Mathematics (6 - 12)

**Title:**Swimming Pool Math

**Description:**Students will use a swimming pool example to practice finding perimeter and area of different rectangles.

**Title:** Soda Cans

**Description:**
This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.
**Standard(s): **

[MA2015] ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)

**Subject:**Mathematics

**Title:**Soda Cans

**Description:**This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Playing with Squares

**Description:**
This reproducible activity sheet, from an Illuminations lesson, prompts students to investigate the meaning of square roots by considering the area of squares and the heights of various stacks of squares.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Playing with Squares

**Description:**This reproducible activity sheet, from an Illuminations lesson, prompts students to investigate the meaning of square roots by considering the area of squares and the heights of various stacks of squares.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Hospital Problem

**Description:**
This reproducible transparency, from an Illuminations lesson, describes an activity in which students must plan where to build a new hospital so that it can serve the needs of three cities.
**Standard(s): **

[MA2015] ALC (9-12) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama)

**Subject:**Mathematics

**Title:**Hospital Problem

**Description:**This reproducible transparency, from an Illuminations lesson, describes an activity in which students must plan where to build a new hospital so that it can serve the needs of three cities.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Circle Packing

**Description:**
In this unit of three Illuminations lessons, students explore circles. In the first lesson students apply the concepts of area and circumference to explore arrangements for soda cans that lead to a more efficient package. In the second lesson they then experiment with three-dimensional arrangements to discover the effect of gravity on the arrangement of soda cans. The final lesson allows students to examine the more advanced mathematical concept of curvature. There are also links to online interactives that are used in the lessons.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Circle Packing

**Description:**In this unit of three Illuminations lessons, students explore circles. In the first lesson students apply the concepts of area and circumference to explore arrangements for soda cans that lead to a more efficient package. In the second lesson they then experiment with three-dimensional arrangements to discover the effect of gravity on the arrangement of soda cans. The final lesson allows students to examine the more advanced mathematical concept of curvature. There are also links to online interactives that are used in the lessons.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Circle Packing and Curvature

**Description:**
In this lesson, one of a three-part unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Circle Packing and Curvature

**Description:**In this lesson, one of a three-part unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Cubes Everywhere

**Description:**
In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through real-life applications. Students are given the opportunity to build and take apart structures based on cubes.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Cubes Everywhere

**Description:**In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through real-life applications. Students are given the opportunity to build and take apart structures based on cubes.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Hospital Locator

**Description:**
In this Illuminations lesson, students begin with a problem in a real-world context to motivate the need to construct circumcenters and then incenters of triangles. Students must make sense of these constructions in terms of bisecting sides and angles. There are links to student interactives and other resources.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Hospital Locator

**Description:**In this Illuminations lesson, students begin with a problem in a real-world context to motivate the need to construct circumcenters and then incenters of triangles. Students must make sense of these constructions in terms of bisecting sides and angles. There are links to student interactives and other resources.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Soda Cans

**Description:**
In this lesson, one of a three-part unit from Illuminations, students investigate various designs for packaging soda cans and use geometry to analyze their designs. Students work to create more efficient arrangements that require less packaging material than the traditional rectangular arrays. In addition, there are links to online activity sheets and other related resources.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Soda Cans

**Description:**In this lesson, one of a three-part unit from Illuminations, students investigate various designs for packaging soda cans and use geometry to analyze their designs. Students work to create more efficient arrangements that require less packaging material than the traditional rectangular arrays. In addition, there are links to online activity sheets and other related resources.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Soda Rack

**Description:**
In this lesson, one of a three-part unit from Illuminations, students consider the arrangement of cans placed in a bin with two vertical sides and discover an interesting result. They then prove their conjectures about the interesting results. In addition, there are links to online activity sheets and other related resources.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Soda Rack

**Description:**In this lesson, one of a three-part unit from Illuminations, students consider the arrangement of cans placed in a bin with two vertical sides and discover an interesting result. They then prove their conjectures about the interesting results. In addition, there are links to online activity sheets and other related resources.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Symmetries III

**Description:**
This lesson, from Illuminations, helps students to understand how translations work and what happens when two or more translations are applied one after the other. Students discover that all band ornaments have translational symmetry and all wallpaper patterns have translational symmetry in at least two directions.
**Standard(s): **

[MA2015] MI1 (9-12) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)

**Subject:**Mathematics

**Title:**Symmetries III

**Description:**This lesson, from Illuminations, helps students to understand how translations work and what happens when two or more translations are applied one after the other. Students discover that all band ornaments have translational symmetry and all wallpaper patterns have translational symmetry in at least two directions.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Triangula Island Overhead

**Description:**
This reproducible transparency, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular polygon such that the sum of the distances to each side is a minimum.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Triangula Island Overhead

**Description:**This reproducible transparency, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular polygon such that the sum of the distances to each side is a minimum.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Triangula Island

**Description:**
This student reproducible, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular triangle such that the sum of the distances to each side is a minimum.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Triangula Island

**Description:**This student reproducible, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular triangle such that the sum of the distances to each side is a minimum.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Robot Sketcher

**Description:**
In this student interactive, from Illuminations, students can build compound arms having multiple joints of two types: one that rotates and is typical of rotating motors, and one that slides and is typical of hydraulic lifts. A circle is used to represent a rotating joint, and a rectangle is used to represent a sliding joint.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Robot Sketcher

**Description:**In this student interactive, from Illuminations, students can build compound arms having multiple joints of two types: one that rotates and is typical of rotating motors, and one that slides and is typical of hydraulic lifts. A circle is used to represent a rotating joint, and a rectangle is used to represent a sliding joint.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Hospital Locator

**Description:**
In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities.
**Standard(s): **

[MA2015] MI1 (9-12) 11: Describe the development of mathematical tools and their applications. (Alabama)

**Subject:**Mathematics

**Title:**Hospital Locator

**Description:**In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Soccer Problem

**Description:**
This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Soccer Problem

**Description:**This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12